Electrical network system



Dec. 17, 1935. 'N. WIENER EI'AL 2,024,900

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ELECTRICAL NETWORK SYS TEM Filed Sept; 2) 1931 16 Sheets-Sheet 9 c, L; R, G R C R 0 R Al' l n I n. ll n All ll AnJ m I m a v Dec. 17, 1935. N w|ENER r AL 2,024,900

ELECTRICAL NETWORK SYSTEM A TTOR/VEY Dec. 17, 1935.

ELECTRICAL NETWORK SYSTEM N. WIENER ET AL Filed Sept. 2, i931 '16 Sheets-Sheet 11 INVENTORJ Dec. 17, 1935. N. WIENER ET AL ELECTRICAL NETWORK SYSTEM 16 Sheets-Sheet 12 Filed Sept. 2, 1931 IN V15 N TOR! Yuk-Win 1 cc lVarer-f M'ener N. WIENER ETAL ELECTRICAL NETWORK SYSTEM Fi'led Sept. 2, 1931 Dee. 17, 1935.

TTOR NE Y Flyu/ Dec. 17, 1935 N. WiE NER E'rAL ELECTRICAL NETWORK SYSTEM Filed Sept. 2, 1931 l6 Sheet s-S heet 14 .u N u n n 13m um A h s k N k u m w w k m H-\ Q Q m N k W? m ugul w k h (MPG-1 In N Q mi kn" M I A 1N VENTORI Yuk-Hilly Lee AAA AAA II Dec. 1 7, 1935; w N T I 2,024,900

ELECTRICAL NETWORK SYSTEM Filed Sept. 2; 1931 16 Sheets- Sheet 15' 7 .36 F7 34 Dec. 17, 1935. N. WIENER EI'AL v 9 ELECTRICAL NETWORK SYSTEM Filed Spt. 2/1931 1s Sheets-Sheet l6 ATTORNEY Patented Dec. 17, 1935 PATENT OFFICE ELECTRICAL NETWORK- SYSTEM Norbert Wiener, Belmont, and Yuk-Wing Lee, Boston, Mass. 1

Application September 2, 1931, Serial No. 560,716

29 Claims.

This invention relates to electrical corrective network systems, and particularly to a new type of electrical network, and to a new method of computing the constants and values of the respective elements of a network system.

In various technical problems, especially in the signalling and communications fields, it is desirable to construct electrical networks having such characteristics that they will pass, or partially or wholly obstruct, any desired electrical vibrations. Difficulty has been experienced in the past in constructing a network having the desired characteristics of control admittance to specified.

vibration frequencies, and ease and convenience of computation and adjustment.

An object of this invention is to construct an electrical network adapted to preliminary computation of circuit constants for desired network characteristics.

Another object of this invention is to combine a plurality of network elements into a single filter structure having predetermined network characteristics.

Still another object of this invention is to provide a network system having a predetermined admittance curve through a given vibration frequency range, certain of said frequencies being very slightly attenuated and others of said frequencies being partially or entirely attenuated.

Still another object of this invention is to adjust the attenuation of electrical vibrations of a plurality of frequencies in a predetermined ratioaccording to the frequency.

A further object of this invention is to assemble in a network system a plurality of adjustable members adapted to modify adjustably the transmission and attenuation characteristics of thenetwork.

A still further object is to adjust a plurality of elements in a network system according to computations whereby a desired network characteristic can be obtained.

Still another object is to match the characteristics of a networksystem to predetermined required characteristics by computation and. adjustment of adjustable members according to the values thereof indicated by the computation.

Still another object of this invention is to adjust a single network system to a transmission produce any desired degree of attenuation of any vibration frequency over a given range.

In the prior art of electricalnetwork systems, it has been common to construct simple systems adapted to pass a desired vibration frequency band and to attenuate substantially and completely all other frequencies or to pass only vibra- I tion frequencies above' a given value or below a given value, or to produce a partial attenuation of. certain desired frequencies, which systems, however, are not subject to adjustment nor conveniently adapted to preliminary computationof the required electrical values.

This invention provides an electrical network system adapted to produce any desired degree of attenuation of any desired frequency, and any desired ratio between the degrees of attenuation of various frequencies, and is adapted to adjustment of the attenuation characteristics by simple adjustment of simple elements in the network, such as potentiometer resistances. This network system thus-is adapted to produce an attenuation curve which is a close approximation within a very small percentage limit of a desired characteristic curve; it being possible by simple adjustment of variable members of the system to obtain any desired curve of attenuation with respect 9; to frequency. The invention further provides a network system, and means for computing the values of components therein, .by which, the values of the components when adjusted to the computed value produce a network system adapted to reproduce accurately the desired network characteristics.

The network effect is obtainedflby an adjustment of phase relationships and magnitude of the electrical vibrations, which adjustments may be upon the basis of preliminary computations to produce the desired network characteristics.

Other objects and structural details of this invention will be apparent from the following description when read in connection with the accompanying figures, wherein:

Figure 1 illustrates a method of combining the transfer admittances of symmetrical networks linearly in connection with the general theory of this invention.

Figures 2 to 4 illustrate the connections used in defining the admittances A, B, and C.

Figures 5 to 6 illustrate tandem connections used in the general theory of this invention.

Figure '7 illustrates a set of lattice'networks.

Figures 8 to 10 illustrate some different forms of four-terminal networks of this invention.

Figure 11 illustrates a voltage ratio characteristic of the network shown in Figure 12.

Figure 12 illustrates particular values of the 55 network shown in Figure 10 for the voltage ratid characteristic shown in Figure 11.

Figure 13 illustrates a resonant lattice network,

Figures 14 to 16 illustrate some resonant fourterminal networks of this invention.

Figures 17 to 18 illustrate some different forms of four-terminal networks of this invention.

Figure 19 illustrates two simple networks used as basis for building up one type of four-terminal networks of this invention.

Figures 20 to 23 illustrate some different forms of four-terminal networks ofthis invention.

Figure 24 illustrates a method of deriving a twoterminal network of preassigned characteristic from a four-terminal network of designable characteristic.

Figure 25 illustrates a method of increasing the driving point conductance of a network without affecting its transfer admittance.

Figures 26 to 33 illustrate some different fo of two-terminal networks of this invention.

Figures '34 to 35 illustrate a methodof deriving two-terminal networks of preassigned characteristics from four-terminal networks of designable characteristics.

Figure 36 illustrates two sets of two-temiinal netvlggrks for the synthesis of two-terminal networ Figure 37 illustrates one form of two-termina networks of this invention.

Figure 38 illustrates two simple circuits from which a two-terminal network of this invention may be built up.

Figure 39 illustrates a two-terminal network of this invention.

Figure 40 is a diagrammatic view illustrating one specific application of the invention to a network including amplifier means.

It is known in the electric circuit theory that the Laplace transform f:f(x)e""=dx of a function fix) vanishing to the left of the origin, is a functionanalytic over the right half of the complex plane, and satisfying appropriate conditions at infinity. Since the admittance function of a network is a function analytic over the right half of the complex plane, it is possible to expand this function in" terms of the Laplace transforms of a complete set of functions defined for positive values of the argument. If theLaplace transforms represent the admittances of a set of known networks, and further, if it is possible to combine the admittances linearly, then the proper combination of these networks will yield a network with any desired admittance function. If we put u=ziw, where our Laplace transformation determines and is determined by a Fourier transformation.

We shall write A for a-b f when a and b are real, and

We shall further simplify F(:c) into F(a:) A class of functions Fn(w) with complex values, having the properties 7' F ,,,(0)I' ,,(w)dw= 0,111 n and 1 is said to'be a. normal and. orthogonal class of functions over the interval and'further if If Fn(w) are the Fourier transforms of a complete set of functions vanishing to the left of the origin, then Y(w) may be taken to represent an admittance function and is expanded in terms of a complete set of normal and orthogonal functions. It is evident that if Fn(w) represent the admittances of a set of known networks, any desired physically realizable quadratically summable admittance function Y(w) may be obtained by a linear combination of the networks.

The linear combination of transfer admittances of symmetrical networks is possible. Thus in Figure 1; if J K, L,-are four-terminal networks symmetrical with respect to their horizontal axes, as indicated in the figure and are connected to a common generator, then the short circuits connecting the output terminalsv of every network, having the same voltage both in magnitude and in phase, at all frequencies with reference to the generator, may be connected together without creating-any interactions among the networks. The current at the junction S is the algebraic sum of the currents from all of the individual networks and their signs depend upon the polarity of the terminals. Hence 'we have here a method to combine transfer admittances linearly. In

the first instance, this leads to a short-circuit transfer admittance.

In order to introduce loads, generator impedances, and other networks into both ends, use will be made of some circuit equations. These equations may be stated as follows: Let A= driving-point admittance of a four-terminal network across terminals I and 2 with terminals 3 and 4 short-circuited as indicated in Fig. 2; let C=driving-point admittance of the network across terminals 3 and 4 with terminals I and 2 short-circuited as shown in Figure 3, and let B=transfer admittance of the network with the connections of Figure 4. These admittances are of complex values, and are functions of the frequency. Then, if two networks I and 2 are connected in tandem as shown 'inFigure 5, the three admittances A0, Bo, and Co of the combination taken as one single network, that is, the four terminals at the extreme ends of the system are now taken as those of the new network, will be B 3 A0=,A! m

and I Afi' 6) The subscripts I and 2 indicate the networks to which the quantities belong. When three networks are connected in tandem, as Figure 6 shows, then the over-all admittances .A'o, 3'0, and Co of the triple combination (the four terminals at the extreme ends of the We see that the transfer admittances of thesystem are taken as those of the new network) are 1! 1 1 6' a,,---; 0 Real part of Y tan d0 and upon the determination'of the coefiicients in the usual manner, that is,

r. 2 1 0' I I Jlilmagmary part of Y('\/ tan 2 )]sm :10 d0 (14) To find a complete set of networks by which we synthesize any desired network, we have two possibllities. One possibility is to form a complete set of networks and then orthogonalize the set of functions representing the transfer admittances of the networks. This follows from the fact that a normal and orthogonal complete system of functions can, by the process of orthogonalization, be determined from a complete sequence of linearly independent functions, and such a system is a linear combination of the given functions. Due to the linear character of the combinations, the final design of a network will be composed'of a set of networks which are non-orthogonal; that is, the theory of orthogonal functions resulting from linear combinations of the transfer admittances of the component networks may be used in computing the composed networks even though this is physically realized as a physical combination of the unorthogonalized component networks. The other possibility is to find a complete set of networks whose transfer admittances form a set of normal and orthogonal functions.

As an example of the first method, let us consider the set of lattice networks shown in Figure 7. The letter Z represents an impedance. These networks are well known for their phase correctting properties. The transfer admittance Bn at the terminating impedance with 11. sections between this and the generator is C' (cos -''j sin :18)

Here

which may be most easily donegraphically, with the aid ofa harmonic analyzer, a network may be designed to yield the required characteristic. The structure of such a network is illustrated in Fig. 8. The networks between which the designed network operates are taken into consideration by Equations ('7), (8) and (9).' Due to the pureresistance character of the lattice network looking from any junction toward either end, the set of lattice networks may be combined to form a single network such as Fig. 9 illustrates. The second section corresponds to a negative term in a series. The value of the inductances, the capacitances, and the resistances of this network are the results of combination in the usual manner, that is,

1 L etc.

There is another method of combination by which we may add voltages instead of currents leading into an open circuit. This is illustratedv in Fig. 10. Each member of the, set of networks is terminated into its image impedance through a transformer instead of a direct termination. 55 In this manner, the values of the inductances may be made to vary from section to section, if n is the number of sections, in the order 1 L n n-- 1 n- 2 beginning with the first section, and the capacitances in the order n,n-1,n 2, 1. The resistance into which the first section terminates is i n+1 R being the image impedance (pure resistance) I of the set of networks before combination, and 70 providing for the constant term in the. Fourier series. For example, if the network consists of four sections, the inductances may have the values L1=25 mh., L2=331/3 mh., Ls=50 mh., and L4=100 mh. (mh.:millihenrys); and the capacitances may have the values C1=0.4 mfd., C2=O.3 mfd., Ca=0.2.mfd., and C4=0.1 mfd. (mfd.=microfarads). The resistance adjacent to the first section is 1 L 1 lOOX 10' /g- X 200 ohms. As the image impedance of each network before combination is 1,000 ohms of pure resistance, each transformer loaded witha resistance should offer this amount of resistance. The transformers may have the same ratio, and if this ratio is unity, one of the transformers may be eliminated. A Fourier series is represented by proper connections on the resistance terminations of the transformers. Each coeflicient is proportional to the amount of resistance across which connections are made, and its sign depends on the polarit y of the connections. The voltage across the extreme terminals is the algebraic sum of the component voltages. Since the image impedances of the set of networks is a pure resistance, the voltage across each terminal resistance is directly proportional to the transfer admittance. A network of this sort has a great variety of designable characteristics with only very simple adjustments in the resistance terminations. Fig. '11

gives a voltage ratio characteristic ofthe network shown in Fig. 12 designed by the above method.

The networks that'have been discussed are a non-resonant type. Similar treatments may be extended to the resonant type. A resonant lattice network is shown in Fig. 13. The transfer admittance 3" of this network at the terminate ing impedance with n sections between this and the generator is Similarly to the previous case, a transfer admittance Y(w) may be represented by the Fourier series Y(w)=2b,.(cos n0"-j sin n0") 1i=0 where w and 0" are related by (16).

The methods of connectionare identical with those in the previous case. The only vdiflerence in the two cases with regard to the even harmonics is in the angle 0 In the former'case, the interval is (0, 1r), and in the latter 0, 2r), covering the same frequency range (0, Figures ,14 to 16 illustrate networks of the resonant type. This network may be used when the odd harmonics in the required network characteristic as a func-- tion of 0" are negligible. To supply such odd harmonics as may be needed, a network substantially odd in 0" may be formed by placing in tandem to a network of the type just discussed a one-stage lattice network so designed as to have an antiresonant point at By combining this network in parallel with a resonant network of the sort just described, we

obtain a substantially universally applicable type of resonant network. The difference in the distribution of the frequency in the two angle intervals gives a difierence in the two expansions of a given function, thus making one kind of network better suited tosome problems than the other.

The second method in finding a set of fundamental networks for the synthesis of networks with specified properties is to find a complete set of networks whose transfer admittances form a set of normal and orthogonal functions. We shall describe an example of this method of 1 synthesis. Consider the functions Q. 8) where the functions Qn(-'B) is Pn(2;c-1), and Pn (w) is the nth Legendre polynominal in w. Here It is a positive constant.

Equation 18 is written as indicated above for the following reason:

Let Hn(w) be the Fourier transforms of (18). Then, if an admittance function Y (to) is The first nine terms of Hn(w) are 1 meo /a 

